Characterisation and identification of chaotic dynamical systems

Shin, Kihong (1996) Characterisation and identification of chaotic dynamical systems. University of Southampton, Doctoral Thesis.

Abstract

Chaotic systems have been widely investigated during the past couple of decades. Specially, fractal dimensions and Lyapunov exponents have been investigated as quantitative measures of chaotic systems. However, very few articles have been reported concerning how these measures are related to system parameters.

This thesis is concerned with system identification and parameter estimation of non-linear dynamical systems exhibiting chaotic motion. Three main contributions of the work are: the development of methods based on Lyapunov exponents for the estimation of parameters characterising dissipation of a non-linear oscillator; the application of the force-state mapping method to chaotic systems: the incorporation of new noise reduction techniques. Specifically, the following aspects are considered:

- Numerical aspects of discretisation of continuous systems in simulation with particular reference to the bilinear mapping

- phase portrait reconstruction using the method of delays and Singular Value Decomposition

- investigation of the concept of the Instantaneous Lyapunov Exponent and its relation to energy dissipation

- noise reduction for chaotic time series using Singular Value Decomposition

- the development of a 'pseudo' force-state mapping method from reconstructed phase portraits

- the application of the methods to an experimental mechanical oscillator.

This record has no associated files available for download.

Contributors

Download statistics